The real part of the conductivity (absorption) of the Hubbard model at strong coupling is studied... more The real part of the conductivity (absorption) of the Hubbard model at strong coupling is studied using exact diagonalization. The low-frequency absorption band which appears in the doped system is examined in both the standard t-J model and in the strong coupling limit of the Hubbard model which includes three-site spin-dependent hopping terms. The conductivity is shown to differ markedly in the two models, with the three-site terms being essential to obtain reasonable agreement with the Hubbard model.
In most theoretical papers written on the properties of polyacetylene the bond alternation is ass... more In most theoretical papers written on the properties of polyacetylene the bond alternation is assumed to arise from the Peierls-instability. This description requires a certain value for the electron-lattice coupling parameter α We discuss the discrepancies found when the electron-lattice coupling is estimated from various experimental quantities for substances as ethane, benzene, ethylene and intercalated graphite. The role of correlation will be included in our discussion.
We consider a class of one-dimensional compass models with antisymmetric Dzyaloshinskii-Moriya ex... more We consider a class of one-dimensional compass models with antisymmetric Dzyaloshinskii-Moriya exchange interaction in an external magnetic field. Based on the exact solution derived by means of Jordan-Wigner transformation, we study the excitation gap, spin correlations, ground state degeneracy and critical properties at phase transitions. The phase diagram at finite electric and magnetic field consists of three phases: a ferromagnetic, a canted antiferromagnetic and a chiral phase. Dzyaloshinskii-Moriya interaction induces an electrical polarization in the ground state of the chiral phase, where the nonlocal string order and special features of entanglement spectra arise, while strong chiral correlations emerge at finite temperature in the other phases and are controlled by a gap between the nonchiral ground state and the chiral excitations. We further show that the magnetoelectric effects in all phases disappear above a typical temperature corresponding to the total bandwidth of the effective fermionic model. To this end we explore the entropy, specific heat, magnetization, electric polarization, and the magnetoelectric tensor at finite temperature. We identify rather peculiar specific heat and polarization behavior of the compass model which follows from highly frustrated interactions.
We investigate the phase diagram and the spin-orbital entanglement of a one-dimensional SU(2)⊗XXZ... more We investigate the phase diagram and the spin-orbital entanglement of a one-dimensional SU(2)⊗XXZ model with SU(2) spin exchange and anisotropic XXZ orbital exchange interactions and negative exchange coupling. As a unique feature, the spin-orbital entanglement entropy in the entangled ground states increases here linearly with system size. In the case of Ising orbital interactions we identify an emergent phase with long-range spin-singlet dimer correlations triggered by a quadrupling of correlations in the orbital sector. The peculiar translational invariant spin-singlet dimer phase has finite von Neumann entanglement entropy and survives when orbital quantum fluctuations are included. It even persists in the isotropic SU(2)⊗SU(2) limit. Surprisingly, for finite transverse orbital coupling the long-range spin singlet correlations also coexist in the antiferromagnetic spin and alternating orbital phase making this phase also unconventional. Moreover we also find a complementary orbital singlet phase that exists in the isotropic case but does not extend to the Ising limit. The nature of entanglement appears essentially different from that found in the frequently discussed model with positive coupling. Furthermore we investigate the collective spin and orbital wave excitations of the disentangled ferromagnetic-spin/ferro-orbital ground state and explore the continuum of spin-orbital excitations. Interestingly one finds among the latter excitations two modes of exciton bound states. Their spin-orbital correlations differ from the remaining continuum states and exhibit logarithmic scaling of the von Neumann entropy with increasing system size. We demonstrate that spin-orbital excitons can be experimentally explored using resonant inelastic x-ray scattering, where the strongly entangled exciton states can be easily distinguished from the spin-orbital continuum.
The density response of a doped Mott-Hubbard insulator is discussed starting from the t-J model i... more The density response of a doped Mott-Hubbard insulator is discussed starting from the t-J model in a slave boson 1/N representation. In leading order O(1) the density fluctuation spectra N(q, ω) are determined by an undamped collective mode at large momentum transfer, in striking disagreement with results obtained by exact diagonalization, which reveal a very broad dispersive peak, reminescent of strong spin-charge coupling. The 1/N corrections introduce the polaron character of the bosonic holes moving in a uniform RVB background. The resulting N(q, ω) captures all features observed in diagonalization studies, fulfills the appropriate sum rules, and apart from the broadening of the collective mode shows a new low energy feature at the energy χJ + δt related to the polaron motion in the spinon background. It is further shown that the low energy structure, which is particularly pronounced in (π, 0) direction, describes the strong renormalization and anomalous damping of the highest bond-stretching phonons in La 2−x Sr x CuO 4. Dedicated to Ferdinando Mancini on the occasion of his 60th birthday published in AIP Conference Proceedings 695: "Highlights in Condensed Matter Physics", ed. A. Avella et al.
Using the self-consistent Born approximation we calculate Reiter's wavefunction for a single hole... more Using the self-consistent Born approximation we calculate Reiter's wavefunction for a single hole introduced into the undoped and orbitally ordered ground state of the t-J model with t2g orbital degrees of freedom. While the number of excitations is similar to the spin t-J model for a given J/t, a distinct structure of the calculated wavefunction and its momentum dependence is identified suggesting the formation of a novel type of mobile polarons.
The consequences of the non-Drude charge response in the normal state of cuprates and the effect ... more The consequences of the non-Drude charge response in the normal state of cuprates and the effect of the layered structure on electron-energy loss spectra are investigated, both for experiments in the transmission and the reflection mode. It is shown that in the intermediate doping regime the plasmon resonance has to be nearly critically damped as a result of the anomalous frequency dependence of the relaxation rate. This also implies an unusual low-energy dependence of the loss function. Both facts are consistent with experiments in cuprates. Our study based on the t-J model shows good agreement with measured plasmon frequencies.
Open Problems in Strongly Correlated Electron Systems, 2001
We analyse the dynamical density fluctuation spectra for cuprates starting from the t − J model i... more We analyse the dynamical density fluctuation spectra for cuprates starting from the t − J model in a slave-boson 1/N representation. The results obtained are consistent with diagonalization studies and show novel low-energy structure on the energy scale J + δt due to the correlated motion of holes in a RVB spin liquid. The low-energy response implies an anomalous renormalization of several phonon modes. Here we discuss the renormalization of the highest breathing phonons in La2−xSrxCuO4. 1 1.
The pairing of quasiparticles in a CuO2 plane is studied within a spin polaron formulation of the... more The pairing of quasiparticles in a CuO2 plane is studied within a spin polaron formulation of the t-t ′-J model. Our numerical solution of the Eliashberg equations unambiguously shows d-wave pairing between spin polarons on different sublattices mediated by the exchange of spin-fluctuations, and a strong doping dependence of the quasiparticle bandwidth. The transition temperature Tc is an increasing function of J/t and crosses a maximum at an optimal doping concentration δopt. For the t-J model with J/t = 0.4 we obtain Tc ≃ 0.013t at δopt ≃ 0.2.
We note a typing mistake in Eq. (3) of our paper. The second term, proportional to t IU, must hav... more We note a typing mistake in Eq. (3) of our paper. The second term, proportional to t IU, must have a negative sign, corresponding to Eq. (4). Because of a numerical error in one of our computer programs, wrong values for all E~&~and two wrong values of
We calculate the order parameter m in the infinite-range isotropic-interaction quantum model of a... more We calculate the order parameter m in the infinite-range isotropic-interaction quantum model of antiferromagnetism due to Lieb and Mattis (LM). The Hamiltonian H, in this model contains pure Heisenberg interactions. m is the mean value of the z component m, of the staggered spin per particle I, in the ground state of H& plus a symmetry-breaking term 8& due to an infinitesimal staggered field B in the thermodynamic limit (TL). We find a value of &3 for the ratio r =m lmo, mo being the root-mean-square value of m, ' for B=0 in the TL. m and mo measure, respectively, the spontaneous symmetry breaking and the amount of long-range order in the symmetry-unbroken state. This value is expected on the basis of our recent argument that r =&3 if m, behaves in the TL as a classical vector with no magnitude fluctuationsbehavior that we show holds for the Lieb-Mattis model. The addition to H& of a small easy-axis anisotropic term is also discussed briefly. These studies allow calculation of the size dependence of quantities that we have recently shown to become lower bounds on m in the TL (bounds that are valid for short-range-interaction models as well). In the LM model, low-lying energy eigenstates with excitation energies of order N, where N is the number of spins, form a continuum {with no gap) in the TL. These are closely related to similar states shown to exist for the nearest-neighbor isotropic Heisenberg antiferromagnet. We show that this continuum has a density of states that is O(N); i.e. , it is not extensive.
Results for the single-particle Green s function for the strong-coupling limit of the single-band... more Results for the single-particle Green s function for the strong-coupling limit of the single-band Hubbard model (t-J model) obtained by numerical and analytical methods are discussed. The numerical calculation of the spectral function is performed for small systems of up to 18 sites using the Lanczos method. A detailed analysis of the spectral functions for the t-J model in one and two dimensions is given. We also investigate the effect of the next-nearest-neighbor hopping terms, which appear in order t /V and are omitted in the standard t Jm-odel. The role of quantum fluctuations on the shape of the spectra and the fundamental difference between one and two dimensions is elucidated. In 2D we find evidence for a coherent quasiparticle band of width 2 J with dispersion uk~(J/2) (cos k + cos k") and spin S = 1/2, which emerges at the low-energy edge of the incoherent spectrum. This form of dispersion is due to effective nextnearest-neighbor processes related to spin Hips and agrees with our extension of the approach of Brinkman and Rice to finite J.
An extended multiband Hubbard model of the two-dimensional Cu02 planes of high-T, superconductors... more An extended multiband Hubbard model of the two-dimensional Cu02 planes of high-T, superconductors is examined by exact diagonalization of the Hamiltonian for small clusters with periodic boundary conditions. Holes are shown to bind in the limit of large Cu-site and nearestneighbor Cu-0 Coulomb repulsion. A simple explanation of the source of the binding energy is given in this strong-coupling limit. The more realistic case of relatively weak nearest-neighbor repulsion is also examined, and suggestive evidence is presented that the effective attraction will also exist in the thermodynamic limit for this case.
The real part of the conductivity (absorption) of the Hubbard model at strong coupling is studied... more The real part of the conductivity (absorption) of the Hubbard model at strong coupling is studied using exact diagonalization. The low-frequency absorption band which appears in the doped system is examined in both the standard t-J model and in the strong coupling limit of the Hubbard model which includes three-site spin-dependent hopping terms. The conductivity is shown to differ markedly in the two models, with the three-site terms being essential to obtain reasonable agreement with the Hubbard model.
In most theoretical papers written on the properties of polyacetylene the bond alternation is ass... more In most theoretical papers written on the properties of polyacetylene the bond alternation is assumed to arise from the Peierls-instability. This description requires a certain value for the electron-lattice coupling parameter α We discuss the discrepancies found when the electron-lattice coupling is estimated from various experimental quantities for substances as ethane, benzene, ethylene and intercalated graphite. The role of correlation will be included in our discussion.
We consider a class of one-dimensional compass models with antisymmetric Dzyaloshinskii-Moriya ex... more We consider a class of one-dimensional compass models with antisymmetric Dzyaloshinskii-Moriya exchange interaction in an external magnetic field. Based on the exact solution derived by means of Jordan-Wigner transformation, we study the excitation gap, spin correlations, ground state degeneracy and critical properties at phase transitions. The phase diagram at finite electric and magnetic field consists of three phases: a ferromagnetic, a canted antiferromagnetic and a chiral phase. Dzyaloshinskii-Moriya interaction induces an electrical polarization in the ground state of the chiral phase, where the nonlocal string order and special features of entanglement spectra arise, while strong chiral correlations emerge at finite temperature in the other phases and are controlled by a gap between the nonchiral ground state and the chiral excitations. We further show that the magnetoelectric effects in all phases disappear above a typical temperature corresponding to the total bandwidth of the effective fermionic model. To this end we explore the entropy, specific heat, magnetization, electric polarization, and the magnetoelectric tensor at finite temperature. We identify rather peculiar specific heat and polarization behavior of the compass model which follows from highly frustrated interactions.
We investigate the phase diagram and the spin-orbital entanglement of a one-dimensional SU(2)⊗XXZ... more We investigate the phase diagram and the spin-orbital entanglement of a one-dimensional SU(2)⊗XXZ model with SU(2) spin exchange and anisotropic XXZ orbital exchange interactions and negative exchange coupling. As a unique feature, the spin-orbital entanglement entropy in the entangled ground states increases here linearly with system size. In the case of Ising orbital interactions we identify an emergent phase with long-range spin-singlet dimer correlations triggered by a quadrupling of correlations in the orbital sector. The peculiar translational invariant spin-singlet dimer phase has finite von Neumann entanglement entropy and survives when orbital quantum fluctuations are included. It even persists in the isotropic SU(2)⊗SU(2) limit. Surprisingly, for finite transverse orbital coupling the long-range spin singlet correlations also coexist in the antiferromagnetic spin and alternating orbital phase making this phase also unconventional. Moreover we also find a complementary orbital singlet phase that exists in the isotropic case but does not extend to the Ising limit. The nature of entanglement appears essentially different from that found in the frequently discussed model with positive coupling. Furthermore we investigate the collective spin and orbital wave excitations of the disentangled ferromagnetic-spin/ferro-orbital ground state and explore the continuum of spin-orbital excitations. Interestingly one finds among the latter excitations two modes of exciton bound states. Their spin-orbital correlations differ from the remaining continuum states and exhibit logarithmic scaling of the von Neumann entropy with increasing system size. We demonstrate that spin-orbital excitons can be experimentally explored using resonant inelastic x-ray scattering, where the strongly entangled exciton states can be easily distinguished from the spin-orbital continuum.
The density response of a doped Mott-Hubbard insulator is discussed starting from the t-J model i... more The density response of a doped Mott-Hubbard insulator is discussed starting from the t-J model in a slave boson 1/N representation. In leading order O(1) the density fluctuation spectra N(q, ω) are determined by an undamped collective mode at large momentum transfer, in striking disagreement with results obtained by exact diagonalization, which reveal a very broad dispersive peak, reminescent of strong spin-charge coupling. The 1/N corrections introduce the polaron character of the bosonic holes moving in a uniform RVB background. The resulting N(q, ω) captures all features observed in diagonalization studies, fulfills the appropriate sum rules, and apart from the broadening of the collective mode shows a new low energy feature at the energy χJ + δt related to the polaron motion in the spinon background. It is further shown that the low energy structure, which is particularly pronounced in (π, 0) direction, describes the strong renormalization and anomalous damping of the highest bond-stretching phonons in La 2−x Sr x CuO 4. Dedicated to Ferdinando Mancini on the occasion of his 60th birthday published in AIP Conference Proceedings 695: "Highlights in Condensed Matter Physics", ed. A. Avella et al.
Using the self-consistent Born approximation we calculate Reiter's wavefunction for a single hole... more Using the self-consistent Born approximation we calculate Reiter's wavefunction for a single hole introduced into the undoped and orbitally ordered ground state of the t-J model with t2g orbital degrees of freedom. While the number of excitations is similar to the spin t-J model for a given J/t, a distinct structure of the calculated wavefunction and its momentum dependence is identified suggesting the formation of a novel type of mobile polarons.
The consequences of the non-Drude charge response in the normal state of cuprates and the effect ... more The consequences of the non-Drude charge response in the normal state of cuprates and the effect of the layered structure on electron-energy loss spectra are investigated, both for experiments in the transmission and the reflection mode. It is shown that in the intermediate doping regime the plasmon resonance has to be nearly critically damped as a result of the anomalous frequency dependence of the relaxation rate. This also implies an unusual low-energy dependence of the loss function. Both facts are consistent with experiments in cuprates. Our study based on the t-J model shows good agreement with measured plasmon frequencies.
Open Problems in Strongly Correlated Electron Systems, 2001
We analyse the dynamical density fluctuation spectra for cuprates starting from the t − J model i... more We analyse the dynamical density fluctuation spectra for cuprates starting from the t − J model in a slave-boson 1/N representation. The results obtained are consistent with diagonalization studies and show novel low-energy structure on the energy scale J + δt due to the correlated motion of holes in a RVB spin liquid. The low-energy response implies an anomalous renormalization of several phonon modes. Here we discuss the renormalization of the highest breathing phonons in La2−xSrxCuO4. 1 1.
The pairing of quasiparticles in a CuO2 plane is studied within a spin polaron formulation of the... more The pairing of quasiparticles in a CuO2 plane is studied within a spin polaron formulation of the t-t ′-J model. Our numerical solution of the Eliashberg equations unambiguously shows d-wave pairing between spin polarons on different sublattices mediated by the exchange of spin-fluctuations, and a strong doping dependence of the quasiparticle bandwidth. The transition temperature Tc is an increasing function of J/t and crosses a maximum at an optimal doping concentration δopt. For the t-J model with J/t = 0.4 we obtain Tc ≃ 0.013t at δopt ≃ 0.2.
We note a typing mistake in Eq. (3) of our paper. The second term, proportional to t IU, must hav... more We note a typing mistake in Eq. (3) of our paper. The second term, proportional to t IU, must have a negative sign, corresponding to Eq. (4). Because of a numerical error in one of our computer programs, wrong values for all E~&~and two wrong values of
We calculate the order parameter m in the infinite-range isotropic-interaction quantum model of a... more We calculate the order parameter m in the infinite-range isotropic-interaction quantum model of antiferromagnetism due to Lieb and Mattis (LM). The Hamiltonian H, in this model contains pure Heisenberg interactions. m is the mean value of the z component m, of the staggered spin per particle I, in the ground state of H& plus a symmetry-breaking term 8& due to an infinitesimal staggered field B in the thermodynamic limit (TL). We find a value of &3 for the ratio r =m lmo, mo being the root-mean-square value of m, ' for B=0 in the TL. m and mo measure, respectively, the spontaneous symmetry breaking and the amount of long-range order in the symmetry-unbroken state. This value is expected on the basis of our recent argument that r =&3 if m, behaves in the TL as a classical vector with no magnitude fluctuationsbehavior that we show holds for the Lieb-Mattis model. The addition to H& of a small easy-axis anisotropic term is also discussed briefly. These studies allow calculation of the size dependence of quantities that we have recently shown to become lower bounds on m in the TL (bounds that are valid for short-range-interaction models as well). In the LM model, low-lying energy eigenstates with excitation energies of order N, where N is the number of spins, form a continuum {with no gap) in the TL. These are closely related to similar states shown to exist for the nearest-neighbor isotropic Heisenberg antiferromagnet. We show that this continuum has a density of states that is O(N); i.e. , it is not extensive.
Results for the single-particle Green s function for the strong-coupling limit of the single-band... more Results for the single-particle Green s function for the strong-coupling limit of the single-band Hubbard model (t-J model) obtained by numerical and analytical methods are discussed. The numerical calculation of the spectral function is performed for small systems of up to 18 sites using the Lanczos method. A detailed analysis of the spectral functions for the t-J model in one and two dimensions is given. We also investigate the effect of the next-nearest-neighbor hopping terms, which appear in order t /V and are omitted in the standard t Jm-odel. The role of quantum fluctuations on the shape of the spectra and the fundamental difference between one and two dimensions is elucidated. In 2D we find evidence for a coherent quasiparticle band of width 2 J with dispersion uk~(J/2) (cos k + cos k") and spin S = 1/2, which emerges at the low-energy edge of the incoherent spectrum. This form of dispersion is due to effective nextnearest-neighbor processes related to spin Hips and agrees with our extension of the approach of Brinkman and Rice to finite J.
An extended multiband Hubbard model of the two-dimensional Cu02 planes of high-T, superconductors... more An extended multiband Hubbard model of the two-dimensional Cu02 planes of high-T, superconductors is examined by exact diagonalization of the Hamiltonian for small clusters with periodic boundary conditions. Holes are shown to bind in the limit of large Cu-site and nearestneighbor Cu-0 Coulomb repulsion. A simple explanation of the source of the binding energy is given in this strong-coupling limit. The more realistic case of relatively weak nearest-neighbor repulsion is also examined, and suggestive evidence is presented that the effective attraction will also exist in the thermodynamic limit for this case.
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Papers by P. Horsch